Question

a point p(x,y) is shown on the unit circle corresponding to a real number t. find the values of the trigonometric functions at t. the point p is p(-\frac{7}{25},-\frac{24}{25}). a. sin t = -\frac{24}{25} (type an integer or a simplified fraction.) b. cos t = -\frac{7}{25} (type an integer or a simplified fraction.) c. tan t = \frac{24}{7} (type an integer or a simplified fraction.) d. csc t = (type an integer or a simplified fraction.)

Explanation:

Step1: Recall the definition of cosecant

Cosecant is the reciprocal of sine, i.e., $\csc t=\frac{1}{\sin t}$.

Step2: Substitute the value of $\sin t$

Given $\sin t =-\frac{24}{25}$, then $\csc t=\frac{1}{-\frac{24}{25}}$.

Step3: Simplify the expression

$\frac{1}{-\frac{24}{25}}=-\frac{25}{24}$.

Answer:

$-\frac{25}{24}$